Ultra-Kolyvagin systems and non-ordinary Selmer groups

2025/11/11 by David Loeffler, Sarah Livia Zerbes, Loeffler, David +1
Mathematics · #11R23 #11S25 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2511.08793

openalex publication_date 2025/11/11 · openalex created_date 2025/11/14 · openalex updated_date 2026/07/28

Abstract

We develop a machine for bounding Selmer groups of Galois representations via Euler systems in "non-ordinary" settings, using Pottharst's definition of Selmer groups via Robba-ring (φ, Γ)-modules. Our approach relies on Sweeting's interpretation of Kolyvagin derivative classes via non-principal ultrafilters. We apply these results to prove new cases of the cyclotomic Iwasawa main conjecture for non-ordinary Rankin--Selberg convolutions.

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